Place the chicken breasts in a large, sealable plastic bag and flatten them to 1-inch thickness with a mallet or rolling pin.
Once pounded to an even size, pour in the balsamic vinaigrette and marinade, and seal the bag.
Allow the chicken to marinate in the refrigerator for at least 30 minutes or up to 1 hour.
Allow the chicken to room temperature for 10 minutes and drain the excess marinade.
Heat your grill to medium or high and grease well with your favorite oil or spray.
Once the grill is hot, cook the chicken breasts for 8-10 minutes per side or until the middle reaches 165 degrees Fahrenheit internally. If you do not have a meat thermometer, check for doneness by slicing it into the middle of the chicken. A properly cooked chicken is when it is no longer pink, and the juices run clear.
Remove the chicken from the grill, place 2-3 slices of fresh mozzarella on each breast, and then cover with a lid or aluminum foil for 2-3 minutes.
When ready to serve the chicken, top each breast with 2-4 slices of avocado and 1-2 slices of tomato.
Garnish with fresh, chopped basil and drizzle on balsamic glaze, optional, before serving hot.